No, in Santorini you cannot flush toilet paper down the toilet bowl.
As with most places in Greece, toilet paper cannot be flushed down the toilet. You should place the used toilet paper into a special trash bin located next to it. The hosts or hotel staff empty the bin every day and put a new bag in it.
Unfortunately, the sewage system in Greece is not adapted to flushing toilet paper – the pipes are too thin and throwing paper into the toilet may clog them.
In most toilets, a special warning hangs regarding the ban on flushing toilet paper.